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- Title
Copulae: An overview and recent developments.
- Authors
Größer, Joshua; Okhrin, Ostap
- Abstract
Over the decades that have passed since they were introduced, copulae still remain a very powerful tool for modeling and estimating multivariate distributions. This work gives an overview of copula theory and it also summarizes the latest results. This article recalls the basic definition, the most important cases of bivariate copulae, and it then proceeds to a sketch of how multivariate copulae are developed both from bivariate copulae and from scratch. Regarding higher dimensions, the focus is on hierarchical Archimedean, vine, and factor copulae, which are the most often used and most flexible ways to introduce copulae to multivariate distributions. We also provide an overview of how copulae can be used in various fields of data science, including recent results. These fields include but are not limited to time series and machine learning. Finally, we describe estimation and testing methods for copulae in general, their application to the presented copula structures, and we give some specific testing and estimation procedures for those specific copulae. This article is categorized under:Statistical Models > Multivariate ModelsStatistical Models > Semiparametric ModelsStatistical and Graphical Methods of Data Analysis > Multivariate Analysis
- Subjects
DISTRIBUTION (Probability theory); COPULA functions; TIME series analysis; MULTIVARIATE analysis; DATA science; MACHINE learning
- Publication
WIREs: Computational Statistics, 2022, Vol 14, Issue 3, p1
- ISSN
1939-5108
- Publication type
Article
- DOI
10.1002/wics.1557